345 Symmetry Groups in Chemistry and Methods of Matrix Algebra

Thursday, November 5, 2009: 4:00 PM
Santa Fe (Camino Real Hotel)
Marion Lawrence Ellzey Jr., Professor of Chemistry , Department of Chemistry, The University of Texas at El Paso, El Paso, TX
Symmetry has been an integral part of modern chemistry since Dalton postulated that all atoms of the same element are identical. The spherical symmetry of atoms and the Pauli exclusion principle of electrons results in the periodic chart of chemical properties. The symmetry of diatomic molecules gives sigma and pi states. Molecules such as ammonia and methane exhibit point group symmetry. There are three kinds of symmetry groups in chemistry: Lie groups, symmetric groups of permutations and point groups. The latter two are finite groups and closely related. Common to all of these are coupling coefficients. According to the Wigner-Eckart Theorem the matrix elements of irreducible tensorial operators are proportional to coupling coefficents. These concepts have been extended to normalized irreducible tensorial matrices in terms of which arbitrary matrices over symmetry-adapted bases may be expanded. An example is given for a three-vertex graph.